Question

Graph the system of equations to find the solution. Identify the solution and its meaning in the question below.b+u = 182b+u = 32

Answer 1

To graph the functions you can take some values and find the points that belongs to the lines.

Easily, we can take b=0 and find the u value, and then take u=0 and find the b value.

For equation 1: b+u=18

`\begin{gathered} \text{With b=0:} \\ 0+u=18\Rightarrow u=18\Rightarrow The\text{ point is (0,18)} \\ \text{With u=0:} \\ b+0=18\Rightarrow b=18\Rightarrow\text{The point is (18,0)} \end{gathered}`

For equation 2: 2b+u=32

`\begin{gathered} \text{With b=0:} \\ 2\cdot0+u=32\Rightarrow u=32\Rightarrow\text{The point is (0,32)} \\ \text{With u=0}\colon \\ 2b+0=32\Rightarrow b=(32)/(2)=16\Rightarrow\text{The point is (16,0)} \end{gathered}`

You can use that points to draw the lines.

If you graph the lines, you can see that they intersect in a point, that's mean the point satisfy the two equations, and it's the solution of the system.